Precision of the ephemerides of outer planetary satellites

Ephemerides of planetary satellites are needed to address many problems. These ephemerides are used for subsequent observations. A comparison of the available ephemerides with new observations allows the accuracy of the former to be assessed. However, the precision of the ephemerides must be known a priori when solving the tasks. In this paper we formulate and solve the problem of estimating the precision of the ephemerides of outer planetary satellites derived from observations when applied up to the future moments.The methods of assessing the precision of ephemerides involve producing a set of samples of the same ephemeris inferred from observations with different samples of Monte Carlo generated random errors (RO) superimposed onto it. The statistical parameters of simulated observational errors are based on the results of the reduction of real satellite observations. We compute the deviations of the samples of the ephemeris from the standard ephemeris inferred from real observations and adopt the root-mean-square deviation of the apparent coordinates as the precision of the ephemeris. We also use alternative methods: one based on the matrix of covariances of parameter errors (RP), and another one based on bootstrap samples of observations (BS).We use three methods (RO, RP, and BS) to estimate the precision of the ephemerides of all the 107 outer planetary satellites over the 2010-2020 time interval. The precision of the ephemerides of different satellites varies from 0.05 to 4.0 arcsec. For a number of satellites new observations are of vital importance for maintaining the precision of the ephemerides at a level that would allow identification of satellites during the reduction of observations. For some satellites the precision of their ephemerides is of the order of the sizes of their orbits and such satellites can be considered to have been lost. We show that the method of bootstrap samples (BS) can give doubtful results in the cases where there are few observations, which covered a time interval that is shorter than the orbital period of the satellite.Our results suggest obtaining more precise ephemeris making new observations at the times of maximum estimated errors of the ephemeris.All the inferred estimates of the precision of ephemerides are available from the MULTI-SAT ephemeris server: www.imcce.fr/sat (IMCCE), www.sai.msu.ru/neb/nss/index.htm (SAI).     

Astrometric results of observations of mutual occultations and eclipses of the Galilean satellites of Jupiter in 2002-2003

We suggest a new approach and develop an original method for deriving astrometric data from the photometry of mutual occultations and eclipses of planetary satellites. We decide to model not the relative apparent motion of one satellite with respect to another satellite but the deflection of the observed relative motion with respect to the theoretical motion implied by appropriate ephemerides.We have attempted to reduce the results of photometric observations of the Gallilean satellites during their mutual occultations and eclipses in 2002-2003. The data of observation for 319 light curves of 106 mutual events were received from the observers. The reliable 245 light curves were processed with our method. Eighty six apparent relative positions have been obtained.Systematic errors arise inevitably while deriving astrometric data. Most of them are due to factors that are unrelated to the methods for deriving astrometric data. The systematic errors are more likely due to incorrect excluding the effect of background on photometric counts. In the case of mutual occultations, the flux drop is determined to a considerable degree by the ratio of the mean albedos of the two satellites. Some mutual event observations revealed wrong adopted values of the mean albedos.     

Detecting the errors in solar system ephemeris by pulsar timing

Pulsar timing uses planetary ephemerides to convert the measured pulse arrival time at an observatory to the arrival time at the Solar System barycenter(SSB). Since these planetary ephemerides cannot be perfect, a method of detecting the associated errors based on a pulsar timing array is developed. By using observations made by an array of 18 millisecond pulsars from the Parkes Pulsar Timing Array, we estimated the vector uncertainty from the Earth to the SSB of JPL DE421, which reflects the offset of the ephemeris origin with respect to the ideal SSB, in different piecewise intervals of pulsar timing data, and found consistent results. To investigate the stability and reliability of our method, we divided all the pulsars into two groups. Both groups yield largely consistent results, and the uncertainty of the Earth-SSB vector is several hundred meters, which is consistent with the accuracy of JPL DE421. As an improvement in the observational accuracy, pulsar timing will be helpful to improve the solar system ephemeris in the future.     

Evolution of Mercury's obliquity

Mercury has a near-zero obliquity, i.e. its spin axis is nearly perpendicular to its orbital plane. The value of the obliquity must be known precisely in order to constrain the size of the planet's core within the framework suggested by Peale [Peale, S.J., 1976. Nature 262, 765-766]. Rambaux and Bois [Rambaux, N., Bois, E., 2004. Astron. Astrophys. 413, 381-393] have suggested that Mercury's obliquity varies on thousand-year timescales due to planetary perturbations, potentially ruining the feasibility of Peale's experiment. We use a Hamiltonian approach (free of energy dissipation) to study the spin-orbit evolution of Mercury subject to secular planetary perturbations. We can reproduce an obliquity evolution similar to that of Rambaux and Bois [Rambaux, N., Bois, E., 2004. Astron. Astrophys. 413, 381-393] if we integrate the system with a set of initial conditions that differs from the Cassini state. However the thousand-year oscillations in the obliquity disappear if we use initial conditions corresponding to the equilibrium position of the Cassini state. This result indicates that planetary perturbations do not force short-period, large amplitude oscillations in the obliquity of Mercury. In the absence of excitation processes on short timescales, Mercury's obliquity will remain quasi-constant, suggesting that one of the important conditions for the success of Peale's experiment is realized. We show that interpretation of data obtained in support of this experiment will require a precise knowledge of the spin-orbit configuration, and we provide estimates for two of the critical parameters, the instantaneous Laplace plane orientation and the orbital precession rate from numerical fits to ephemeris data. Finally we provide geometrical relationships and a scheme for identifying the correct initial conditions required in numerical integrations involving a Cassini state configuration subject to planetary perturbations.     

Assessment of the resonant perturbation errors in Galilean satellite ephemerides using precisely measured eclipse times

Astrometric satellite positions are derived from timings of their eclipses in the shadow of Jupiter. The 548 data points span 20 years and are accurate to about 0.006 arcsec for Io and Europa and about 0.015 arcsec or better for Ganymede and Callisto. The precision of the data set and its nearly continuous distribution in time allows measurement of regular oscillations with an accuracy of 0.001 arcsec. This level of sensitivity permits detailed evaluation of modern ephemerides and reveals anomalies at the 1.3 year period of the resonant perturbations between Io, Europa and Ganymede. The E5 ephemeris shows large errors at that period for all three satellites as well as other significant anomalies. The L1 ephemeris fits the observations much more closely than E5 but discrepancies for the resonant satellites are still apparent and the measured positions of Io are drifting away from the predictions. The JUP230 ephemeris fits the observations more accurately than L1 although there is still a measurable discordance between the predictions and observations for Europa at the resonance period.     

On the astrometric detection of neighboring planetary systems,II

Extensive testing suggests that astrometric techniques can be employed to detect and study virtually any planetary system that may exist within 40 light years (12.5 parsec) of the Sun. Following the conclusion of Paper I [G. Gatewood, Icarus27 (1976), 1–12], the astrometric group at the Allegheny Observatory began an intensive survey of 20 nearby stars to detect the nonlinear variations in their motion that planetary systems would induce. Several tests conducted to further our understanding of the limitations of this survey indicated that the photographic detector itself is responsible for the majority of the random error. A new photoelectric detector has been designed and a simplified prototype of it successfully tested. The new detector is expected to be able to utilize virtually all of the astrometric information transmitted through the Earth's atmosphere. This is sufficient to determine relative positions to within an accuracy of approximately 1 milliarcsec/hr. Such precisions exceed the design capabilities of the best existing astrometric telescopes, thus a feasibility study has been conducted for the design of an improved instrument. The study concludes that a new ground-based telescope and the new detector combined should be able to study stars as faint as the 17th magnitude with an annual accuracy of a few tenths of a milliarcsecond. However, to obtain the ultimate accuracy possible from current technology, we must place an astrometric system above the Earth's atmosphere. A space-borne instrument utilizing the new detector would in theory have sufficient accuracy to detect any Earth-like planet orbiting any of the several hundred stars nearest the Sun.     

Mutual events of the uranian satellites 2006-2010

The upcoming crossing of the Sun and the Earth through the equatorial plane of the planet Uranus presents an opportunity to observe mutual eclipses and occultations of the uranian satellites. We present predictions for 321 such events from 2006 to 2010. 230 of these events are “nominal” i.e. they are predicted to occur based on the currently available ephemeris while a further 91 “grazing” events are allowable given the positional uncertainties of the satellites. Taking into account the statistical frequency of events that occur too close to the planet, during solar conjunction or are too “shallow” to observe, we conclude that about 150 events should be detectable from different longitudes around the world. We argue that a worldwide campaign of photometric observations of these events will yield, as in the case of the jovian and saturnian systems, high-precision astrometric information on the satellites toward improving their ephemerides as well as the system constants (satellite masses, uranian zonal harmonics, etc.). In addition, mathematical inversion of the lightcurves should permit, subject to the photometric quality and number of observed events, mapping of albedo variegations over the satellite hemispheres that were in darkness during the Voyager 2 encounter with the uranian system in 1985/1986.     

Estimates of dynamic parameters and boundaries of habitable zones of selected stars of the Pulkovo program

A list of selected binary stars is presented that have been observed for several decades using a 26-inch refractor at the Pulkovo Observatory. These stars are at a distance from 3.5 to 25 pc from the Sun. They belong to spectral classes F, G, K, and M. Their masses range from 0.3 to 1.5 solar masses. We have analyzed them as possible parent stars for exoplanets taking into account the physical characteristics of these stars. In view of dynamic parameters and orbital elements that we have obtained by Pulkovo observations, ephemerides of positions for the coming years are calculated. The boundaries of the habitable zones around these stars are calculated. The astrometric signal that depends on the gravitational influence of hypothetical planets is estimated. Space telescopes for astrometric observations with microsecond accuracy can be used to detect Earth-like planets near the closest stars of this program. This paper presents an overview of astrometric programs of searches for exoplanets.     

Comet and asteroid ephemerides for spacecraft encounters

To a significant degree, the success of spacecraft missions to comets and asteroids depends upon the accuracy of the target body ephemerides. In turn, accurate ephemerides depend upon the quality of the astrometric data set used in determining the object's orbit and the accuracy with which the target body's motion can be modelled. Using error analyses studies of the target bodies for the NEAR, Muses-C, Clementine 2, Stardust, and Rosetta missions, conclusions are drawn as to how to minimize target body position uncertainties at the times of encounter, In general, these uncertainties will be minimized when the object has a good number of optical observations spread over several orbital periods. If a target body lacks a lengthy data interval, its ephemeris uncertainties can be dramatically reduced with the use of radar Doppler and delay data taken when the body is relatively close to the Earth. The combination of radar and optical angle data taken at close Earth distances just before a spacecraft encounter can result in surprisingly small target body ephemeris uncertainties.     

High-Precision Ephemerides of Planets—EPM and Determination of Some Astronomical Constants

The latest version of the planetary part of the numerical ephemerides EPM (Ephemerides of Planets and the Moon) developed at the Institute of Applied Astronomy of the Russian Academy of Sciences is presented. The ephemerides of planets and the Moon were constructed by numerical integration in the post-Newtonian metric over a 140-year interval (from 1880 to 2020). The dynamical model of EPM2004 ephemerides includes the mutual perturbations from major planets and the Moon computed in terms of General Relativity with allowance for effects due to lunar physical libration, perturbations from 301 big asteroids, and dynamic perturbations due to the solar oblateness and the massive asteroid ring with uniform mass distribution in the plane of the ecliptic. The EPM2004 ephemerides resulted from a least-squares adjustment to more than 317000 position observations (1913–2003) of various types, including radiometric measurements of planets and spacecraft, CCD astrometric observations of the outer planets and their satellites, and meridian and photographic observations. The high-precision ephemerides constructed made it possible to determine, from modern radiometric measurements, a wide range of astrometric constants, including the astronomical unit AU = (149597870.6960 ± 0.0001) km, parameters of the rotation of Mars, the masses of the biggest asteroids, the solar quadrupole moment J ₂ = (1.9 ± 0.3) × 10⁻⁷, and the parameters of the PPN formalism β and γ. Also given is a brief summary of the available state-of-the-art ephemerides with the same precision: various versions of EPM and DE ephemerides from the Jet Propulsion Laboratory (JPL) (USA) and the recent versions of these ephemerides—EPM2004 and DE410—are compared. EPM2004 ephemerides are available via FTP at ftp://qua-sar.ipa.nw.ru/incoming/EPM2004.__________Translated from Astronomicheskii Vestnik, Vol. 39, No. 3, 2005, pp. 202–213.Original Russian Text Copyright © 2005 by Pitjeva.     

The topography of Iapetus' leading side

We have used Cassini stereo images to study the topography of Iapetus' leading side. A terrain model derived at resolutions of 4-8 km reveals that Iapetus has substantial topography with heights in the range of −10 km to +13 km, much more than observed on the other middle-sized satellites of Saturn so far. Most of the topography is older than 4 Ga [Neukum, G., Wagner, R., Denk, T., Porco, C.C., 2005. Lunar Planet. Sci. XXXVI. Abstract 2034] which implies that Iapetus must have had a thick lithosphere early in its history to support this topography. Models of lithospheric deflection by topographic loads provide an estimate of the required elastic thickness in the range of 50-100 km. Iapetus' prominent equatorial ridge [Porco, C.C., and 34 colleagues, 2005. Science 307, 1237-1242] reaches widths of 70 km and heights of up to 13 km from their base within the modeled area. The morphology of the ridge suggests an endogenous origin rather than a formation by collisional accretion of a ring remnant [Ip, W.-H., 2006. Geophys. Res. Lett. 33, doi:10.1029/2005GL025386. L16203]. The transition from simple to complex central peak craters on Iapetus occurs at diameters of 11±3 km. The central peaks have pronounced conical shapes with flanking slopes of typically 11° and heights that can rise above the surrounding plains. Crater depths seem to be systematically lower on Iapetus than on similarly sized Rhea, which if true, may be related to more pronounced crater-wall slumping (which widens the craters) on Iapetus than on Rhea. There are seven large impact basins with complex morphologies including central peak massifs and terraced walls, the largest one reaches 800 km in diameter and has rim topography of up to 10 km. Generally, no rings are observed with the basins consistent with a thick lithosphere but still thin enough to allow for viscous relaxation of the basin floors, which is inferred from crater depth-to-diameter measurements. In particular, a 400-km basin shows up-domed floor topography which is suggestive of viscous relaxation. A model of complex crater formation with a viscoplastic (Bingham) rheology [Melosh, H.J., 1989. Impact Cratering. Oxford Univ. Press, New York] of the impact-shocked icy material provides an estimate of the effective cohesion/viscosity at . The local distribution of bright and dark material on the surface of Iapetus is largely controlled by topography and consistent with the dark material being a sublimation lag deposit originating from a bright icy substrate mixed with the dark components, but frost deposits are possible as well.     

Spectrophotometry of the small satellites of Saturn and their relationship to Iapetus, Phoebe, and Hyperion

We have obtained broadband spectrophotometric observations of four of the recently discovered small satellites of Saturn (Gladman et al., 2001, Nature 412, 163-166). The new data enable an understanding of the provenance, composition, and interrelationships among these satellites and the other satellites of Saturn, particularly Iapetus, Phoebe, and Hyperion. Temporal coverage of one satellite (S21 Tarvos) was sufficient to determine a partial rotational lightcurve. Our major findings include: (1) the satellites are red and similar in color, comparable to D-type asteroids, some KBOs, Iapetus, and Hyperion; (2) none of the satellites, including those from the “Phoebe Group” has any spectrophotometric relationship to Phoebe; and (3) S21 Tarvos exhibits a rotational lightcurve, although the data are not well-constrained and more observations are required to fit a definitive period. Dust created by meteoritic impacts and ejected from these satellites and additional undiscovered ones may be the source of the exogenous material deposited on the low-albedo side of Iapetus. Recent work which states that the small irregular satellites of Saturn have impacted Phoebe at least 6-7 times in the age of the Solar System (Nesvorny et al., 2003, Astron. J. 126, 398-429), suggests that such collisions may have propelled additional material from both Phoebe and the small irregular satellites toward Iapetus. The accretion of material from outer retrograde satellites may be a process that also occurs on Callisto and the uranian satellites.     

On the orientation of ephemeris reference frames

One may construct complete planetary and lunar ephemerides, referred to the equator and dynamical equinox of some epoch, strictly from ranging data alone. Such an ephemeris would be completely independent from any optical data and therefore independent of any stellar catalogue. By using such an ephemeris to then analyse optical observations, one could theoretically derive many of the pertinent features of the catalogue system to which the optical observations are referred. Such features include the equinox offset, equinox motion and systematic proper motion errors. In practice, the optical observations are used in the fitting process, but essentially the same determinations may be made.This paper presents estimates of the equinox offset and equinox motion of the FK4 as determined by the ephemeris fitting process and compares them with corresponding determinations by Fricke. No significant differences are found. Further, it is indicated how one may also estimate a value for precession and the value of the obliquity from the ephemerides. These' values are also compared with the presently adopted ones.     

Accurate analytical representation of Pluto modern ephemeris

An accurate development of the latest JPL’s numerical ephemeris of Pluto, DE421, to compact analytical series is done. Rectangular barycentric ICRF coordinates of Pluto from DE421 are approximated by compact Fourier series with a maximum error of 1.3 km over 1900–2050 (the entire time interval covered by the ephemeris). To calculate Pluto positions relative to the Sun, a development of rectangular heliocentric ICRF coordinates of the Solar System barycenter to Poisson series is additionally made. As a result, DE421 Pluto heliocentric positions by the new analytical series are represented to an accuracy of better than 5 km over 1900–2050.     

Astrometric observations of the second, third, and fourth satellites of Uranus

The results of astrometric observations of three Uranian satellites, performed at the Ka-Dar observatory from August to October 2005, are presented. In total, 20 satellite positions in the equatorial frame and 14 “satellite minus satellite” relative positions were obtained.     

Cassini RADAR observations of Enceladus, Tethys, Dione, Rhea, Iapetus, Hyperion, and Phoebe

Cassini 2.2-cm radar and radiometric observations of seven of Saturn's icy satellites yield properties that apparently are dominated by subsurface volume scattering and are similar to those of the icy Galilean satellites. Average radar albedos decrease in the order Enceladus/Tethys, Hyperion, Rhea, Dione, Iapetus, and Phoebe. This sequence most likely corresponds to increasing contamination of near-surface water ice, which is intrinsically very transparent at radio wavelengths. Plausible candidates for contaminants include ammonia, silicates, metallic oxides, and polar organics (ranging from nitriles like HCN to complex tholins). There is correlation of our targets' radar and optical albedos, probably due to variations in the concentration of optically dark contaminants in near-surface water ice and the resulting variable attenuation of the high-order multiple scattering responsible for high radar albedos. Our highest radar albedos, for Enceladus and Tethys, probably require that at least the uppermost one to several decimeters of the surface be extremely clean water ice regolith that is structurally complex (i.e., mature) enough for there to be high-order multiple scattering within it. At the other extreme, Phoebe has an asteroidal radar reflectivity that may be due to a combination of single and volume scattering. Iapetus' 2.2-cm radar albedo is dramatically higher on the optically bright trailing side than the optically dark leading side, whereas 13-cm results reported by Black et al. [Black, G.J., Campbell, D.B., Carter, L.M., Ostro, S.J., 2004. Science 304, 553] show hardly any hemispheric asymmetry and give a mean radar reflectivity several times lower than the reflectivity measured at 2.2 cm. These Iapetus results are understandable if ammonia is much less abundant on both sides within the upper one to several decimeters than at greater depths, and if the leading side's optically dark contaminant is present to depths of at least one to several decimeters. As argued by Lanzerotti et al. [Lanzerotti, L.J., Brown, W.L., Marcantonio, K.J., Johnson, R.E., 1984. Nature 312, 139-140], a combination of ion erosion and micrometeoroid gardening may have depleted ammonia from the surfaces of Saturn's icy satellites. Given the hypersensitivity of water ice's absorption length to ammonia concentration, an increase in ammonia with depth could allow efficient 2.2-cm scattering from within the top one to several decimeters while attenuating 13-cm echoes, which would require a six-fold thicker scattering layer. If so, we would expect each of the icy satellites' average radar albedos to be higher at 2.2 cm than at 13 cm, as is the case so far with Rhea [Black, G., Campbell, D., 2004. Bull. Am. Astron. Soc. 36, 1123] as well as Iapetus.     

Saturn’s wayward shepherds: the peregrinations of Prometheus and Pandora

Saturn’s narrow F ring is flanked by two nearby small satellites, Prometheus and Pandora, discovered in Voyager images taken in 1980 and 1981 (Synnott et al., 1983, Icarus 53, 156-158). Observations with the Hubble Space Telescope (HST) during the ring plane crossings (RPX) of 1995 led to the unexpected finding that Prometheus was ∼19° behind its predicted orbital longitude, based on the Synnott et al. (1983) Voyager ephemeris (Bosh and Rivkin, 1996 Science 272, 518-521; Nicholson et al., 1996, Science 272, 509-515). Whereas Pandora was at its predicted location in August 1995, McGhee (2000, Ph.D. thesis, Cornell University) found from the May and November 1995 RPX data that Pandora also deviates from the Synnott et al. (1983) Voyager ephemeris. Using archival HST data from 1994, previously unexamined RPX images, and a large series of targeted WFPC2 observations between 1996 and 2002, we have determined highly accurate sky-plane positions for Prometheus, Pandora, and nine other satellites found in our images. We compare the Prometheus and Pandora measurements to the predictions of substantially revised and improved ephemerides for the two satellites based on an extensive analysis of a large set of Voyager images (Murray et al., 2000, Bull. Am. Astron. Soc. 32, 1090; Evans, 2001 Ph.D. thesis, Queen Mary College). From December 1994 to December 2000, Prometheus’ orbital longitude lag was changing by −0.71° year⁻¹ relative to the new Voyager ephemeris. In contrast, Pandora is ahead of the revised Voyager prediction. From 1994 to 2000, its longitude offset changed by +0.44° year⁻¹, showing in addition an ∼585 day oscillatory component with amplitude Δλ_CR0 = 0.65 ± 0.07° whose phase matches the expected perturbation due to the nearby 3:2 corotation resonance with Mimas, modulated by the 71-year libration in the longitude of Mimas due to its 4:2 resonance with Tethys. We determine orbital elements for freely precessing equatorial orbits from fits to the 1994-2000 HST observations, from which we conclude that Prometheus’ semimajor axis was 0.31 km larger, and Pandora’s was 0.20 km smaller, than during the Voyager epoch. Subsequent observations in 2001-2002 reveal a new twist in the meanderings of these satellites: Prometheus’ mean motion changed suddenly by an additional −0.77° year⁻¹, equivalent to a further increase in semimajor axis of 0.33 km, at the same time that Pandora’s mean motion changed by +0.92° year⁻¹, corresponding to a change of −0.42 km in its semimajor axis. There is an apparent anticorrelation of the motions of these two moons seen in the 2001-2002 observations, as well as over the 20-year interval since the Voyager epoch. This suggests a common origin for their wanderings, perhaps through direct exchange of energy between the satellites as the result of resonances, possibly involving the F ring.     

A new dynamical model for the Uranian satellites

We have developed a new dynamical model of the main Uranian satellites, based on numerical integration and fitted to astrometric observations. Old observations, as well as modern and Voyager observations have been included. This model has provided ephemerides that have already been used for predicting the mutual events during the PHE-URA campaign. It is updated here to improve the prediction of these events. We also tried to assess the real accuracy of our ephemerides by checking the distance differences of the Uranian satellites, using simultaneously our former and new model. It appears that both solutions are very close to each other (within few tens of kilometers), and most probably accurate at the level of few hundred of kilometers. Using new available meridian observations of the Uranian satellites, we have checked the Uranian ephemeris accuracy using DE406. An error of more than 0.1 arcsec on the Uranian position is observed.     

The mass of the Andromeda galaxy

This paper argues that the Milky Way galaxy is probably the largest member of the Local Group. The evidence comes from estimates of the total mass of the Andromeda galaxy (M31) derived from the three-dimensional positions and radial velocities of its satellite galaxies, as well as the projected positions and radial velocities of its distant globular clusters and planetary nebulae. The available data set comprises 10 satellite galaxies, 17 distant globular clusters and nine halo planetary nebulae with radial velocities. We find that the halo of Andromeda has a mass of together with a scalelength of 90 kpc and a predominantly isotropic velocity distribution. For comparison, our earlier estimate for the Milky Way halo is Although the error bars are admittedly large, this suggests that the total mass of M31 is probably less than that of the Milky Way . We verify the robustness of our results to changes in the modelling assumptions and to errors caused by the small size and incompleteness of the data set.
Our surprising claim can be checked in several ways in the near future. The numbers of satellite galaxies, planetary nebulae and globular clusters with radial velocities can be increased by ground-based spectroscopy, while the proper motions of the companion galaxies and the unresolved cores of the globular clusters can be measured using the astrometric satellites Space Interferometry Mission ( SIM ) and Global Astrometric Interferometer for Astrophysics ( GAIA ). Using 100 globular clusters at projected radii 20 R 50 kpc with both radial velocities and proper motions, it will be possible to estimate the mass within 50 kpc to an accuracy of 20 per cent. Measuring the proper motions of the companion galaxies with SIM and GAIA will reduce the uncertainty in the total mass caused by the small size of the data set to 22 per cent.     

Building the cosmic distance scale: from Hipparcos to Gaia

Hipparcos, the first ever experiment of global astrometry, was launched by ESA (European Space Agency) in 1989 and its results published in 1997 (Perryman et al. in Astron. Astrophys. 323:L49, 1997; Perryman & ESA (eds.) in The Hipparcos and Tycho catalogues, ESA SP-1200, 1997). A new reduction was later performed using an improved satellite attitude reconstruction leading to an improved accuracy for stars brighter than 9th magnitude (van Leeuwen & Fantino in Astron. Astrophys. 439:791, 2005; van Leeuwen in Astron. Astrophys. 474:653, 2007a). The Hipparcos Catalogue provided an extended dataset of very accurate astrometric data (positions, trigonometric parallaxes and proper motions), enlarging by two orders of magnitude the quantity and quality of distance determinations and luminosity calibrations. The availability of more than 20 000 stars (22 000 for the original catalogue, 30 000 for the re-reduction) with a trigonometric parallax known to better than 10% opened the way to a drastic revision of our 3-D knowledge of the solar neighbourhood and to a renewal of the calibration of many distance indicators and age estimations. The prospects opened by Gaia, the next ESA cornerstone, planned for launch in 2013 (Perryman et al., in Astron. Astrophys. 369:339, 2001), are still much more dramatic: a billion objects with systematic and quasi simultaneous astrometric, spectrophotometric and spectroscopic observations, about 150 million stars with expected distances to better than 10%, all over the Galaxy. All stellar distance indicators, in very large numbers, will be directly measured, providing a direct calibration of their luminosity and making possible detailed studies of the impacts of various effects linked to chemical element abundances, age or cluster membership. With the help of simulations of the data expected from Gaia, obtained from the mission simulator developed by DPAC (Gaia Data Processing and Analysis Consortium), we will illustrate what Gaia can provide with some selected examples.